The government's plan for a high-speed railway connecting London with Birmingham, Manchester and Leeds is beset by spiralling costs, a lack of expertise and unrealistic delivery timetables, a parliamentary report has concluded.

The public accounts committee (PAC) says the Department for Transport has "not yet presented a convincing case" for building the £50bn HS2 project, which will take 20 years to complete in two phases.

The project, which received support from David Cameron during his G20 trip last week, has been panned by the committee, which found that £185m had already been spent on consultants – a figure that is expected to rise to £500m by the time building work begins in early 2016.

Pointing to the fiasco surrounding the franchise award of the Westcoast mainline in October , the 56-page report, published on Monday, says the department is suffering from a "shortage of the commercial skills it needs to protect taxpayers' interests" and noted that costs for the first phase of the project had risen by almost £5bn to £21.4bn.

On Friday the prime minister threw his weight behind the plans, saying that he was "passionately in favour" of the multibillion-pound scheme, and urged doubters to "think big". Speaking in St Petersburg, where he was attending the G20 summit, Cameron said: "There's an unholy alliance between the Financial Times, Peter Mandelson and Nigel Farage, who want to give up on projects to make our country competitive and fit for the 21st century … We know infrastructure projects can make a massive change to the economic geography of our country."

The report heavily criticises the department's predictions for the project's benefits. It finds that after overestimating economic benefits by £8bn through a double-counting error, the department has forecast smaller rises in commuter numbers than expected. These latest figures have yet to be taken into account by HS2 planners and would push down estimated economic gains.

"So far the department has made decisions based on fragile numbers, out-of-date data and assumptions which do not reflect real life," it said.

Fears were also raised about the government's parliamentary timetable. Describing the deadline for passing HS2 legislation by March 2015 as "unrealistic and overly ambitious", the committee predicted that each month legislation is delayed will cost £7m-£10m.

It said: "The department has yet to demonstrate that this is the best way to spend £50bn on rail investment in these constrained times, that this is the most effective and economic way of responding to future demand patterns, that the figures predicting future demand are robust and credible, and that the improved connectivity between London and regional cities will enhance growth and activity in the regions rather than drawing more activity into London."

Transport secretary Patrick McLoughlin rejected the PAC findings, insisting that the case was "absolutely clear" and that without HS2, key rail routes would be "overwhelmed" by rising passenger numbers. "The project will free up vital space on our railways for passengers and freight, generate hundreds of thousands of jobs, and deliver better connections between our towns and cities," he said.

Speaking on Sky News the day before the report's publication, he said HS2 "was a very central project for the United Kingdom" which would always attract controversy.

"Any big infrastructure project, if you look over the history of the railway altogether, there has been controversy when new lines have been talked about. We haven't built a new railway line north of London for 120 years. We are going to be desperately short of capacity."

The PAC's chair, Margaret Hodge, said the DfT's case was not yet convincing. "It has not yet demonstrated that this is the best way to spend £50bn on rail investment in these constrained times, and that the improved connectivity will promote growth in the regions rather than sucking even more activity into London.

"The pattern so far has been for costs to spiral – from more than £16bn to £21bn plus for phase one – and the estimated benefits to dwindle."

She added that the department was still using "out-of-date data and assumptions which do not reflect real life, such as assuming business travellers do not work on trains using modern technology".

Fellow committee member Richard Bacon, the MP for South Norfolk, said the department owed it to "rail users everywhere to stop itself going down the wrong track" and that the money might be better spent on existing rail lines.

Matthew Sinclair, chief executive of the TaxPayers' Alliance campaign, said the business case for HS2 was weaker than ever: "The sooner the government shunts this white elephant into the sidings for good, the better for the taxpayers who will otherwise be saddled with an eye-watering bill."